75.6.7 problem 7

Internal problem ID [19975]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter V. Homogeneous linear differential equations. Exact equations. Exercises at page 69
Problem number : 7
Date solved : Thursday, October 02, 2025 at 05:04:39 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-x y^{\prime }+y&=\ln \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=x^2*diff(diff(y(x),x),x)-x*diff(y(x),x)+y(x) = ln(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = c_2 x +x \ln \left (x \right ) c_1 +\ln \left (x \right )+2 \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 19

ode=x^2*D[y[x],{x,2}]-x*D[y[x],x]+y[x]==Log[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \log (x)+c_1 x+c_2 x \log (x)+2 \end{align*}

✓ Sympy. Time used: 0.130 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x*Derivative(y(x), x) + y(x) - log(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} x + C_{2} x \log {\left (x \right )} + \log {\left (x \right )} + 2 \]